1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120 Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).

(a) Obtain the reaction function of a firm. Map the function obtained, and graphically represent the Cournot equilibrium in this market.

(b) Obtain this equilibrium again, this time analytically.

(c) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.

(d) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?

(e) Finally, assume that there is one firm with costs C(q) = 30q but two firms with costs C(q) = 45q. Solve the equilibrium again (using the fact that the two firms with equal costs will end up producing the same amount: the symmetry trick). What is the effect on consumer's surplus and total surplus of the higher degree of competition?